Is it possible to export animations/actions separately from Blender to Unity
If you're exporting to FBX manually from Blender, the checkbox Baked Animation will save the animation to the file. Keep in mind that you do have to select the Armature object type to export (and exclude everything else). The animations reference the armature for keyframes.
Alternatively, you can do this via Python script with the command:
bpy.ops.export_scene.fbx(... use_anim=True, ....)
I actually just published a blog post about exporting multiple FBX files for the purposes of importing into Unity. It's only Part 1, but I should have Part 2 written up sometime soon!
http://undertheweathersoftware.com/building-character-customization-part-1